Viscoelastic Materials

Lakes, Roderic S.

doi:10.1017/cbo9780511626722

Cited by 760 publications

(348 citation statements)

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“…for an ideally viscous liquid [12]. In the end of systole arterial pressure drops sharply and the negative pressure propagates distally.…”

Section: Discussionmentioning

confidence: 99%

Resistive Factors of the Blood Flow and Energy Distribution in the Body

Beraia¹,

Beraia²

2017

Health

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Purpose of the study is to identify the reason for the formation of the resistive factors in blood flow: inertial flow and turbulence in large arteries and increasing viscosity in the venous blood. Methods and Materials: Blood flow velocities were studied in the different sites of the large vessels in 35 normal adults (15 men, 20 women, age 21 -49 years) with the use of Magnetic Resonance Angiography. Blood radiodensity (HU) was measured by the CT scanner. Blood flow pulsatility, resistivity indexes were carried out with the Duplex US. Results: Resistive and pulsatility indexes for the ascending aorta are 0.96 ± 0.07 and 3.14. ± 1.7, abdominal aorta 0.91 ± 0.07 and 2.7 ± 1.3, carotid artery 0.74 ± 0.07 and 2.04 ± 0.53, pulmonary trunk 0.74 ± 0.11 and 1.49 ± 0.37, inferior vena cava 0.32 ± 0.21 and 0.69 ± 0.37. Blood radio density (in HU) in the ascending aorta is 57.3 ± 3.5, distal thoracic aorta 25.7 ± 3.1, and inferior vena cava 59.3 ± 3.3. Pulsation of the peak velocity is expressed at the external wall of the isthmus of aorta at the end of systole. Conclusion: Heart energy is stored in the elastic deformation of the blood cells and arterial walls, in kinetic energy of the blood flow, entropy of the system. Inertial blood flow due to the frequency dispersion in the arteries, transforms to the flow with the high fluidity in capillaries. Gibbs free energy increases, enabling spontaneous chemical reaction to proceed across the cell membrane. Process is altered in the venous blood. Changes in resistance express transformation of the energy in the substance.

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“…for an ideally viscous liquid [12]. In the end of systole arterial pressure drops sharply and the negative pressure propagates distally.…”

Section: Discussionmentioning

confidence: 99%

Resistive Factors of the Blood Flow and Energy Distribution in the Body

Beraia¹,

Beraia²

2017

Health

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“…Development of this model is described in [6], as well as in standard viscoelastic theory [18,20,21,22,25,27]. It is worth noting that the linear system (1) with (2) is found to give a reasonable approximation to the experimental data provided by QMUL.…”

Section: X=0mentioning

confidence: 91%

Material parameter estimation and hypothesis testing on a 1D viscoelastic stenosis model: Methodology

Banks

Kenz

et al. 2013

Journal of Inverse and Ill-Posed Problems

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Non-invasive detection, localization and characterization of an arterial stenosis (a blockage or partial blockage in the artery) continues to be an important problem in medicine. Partial blockage stenoses are known to generate disturbances in blood flow which generate shear waves in the chest cavity. We examine a one-dimensional viscoelastic model that incorporates Kelvin-Voigt damping and internal variables, and develop a proof-of-concept methodology using simulated data. We first develop an estimation procedure for the material parameters. We use this procedure to determine confidence intervals for the estimated parameters, which indicates the efficacy of finding parameter estimates in practice. Confidence intervals are computed using asymptotic error theory as well as bootstrapping. We then develop a model comparison test to be used in determining if a particular data set came from a low input amplitude or a high input amplitude; this we anticipate will aid in determining when stenosis is present. These two thrusts together will serve as the methodological basis for our continuing analysis using experimental data currently being collected.Mathematics Subject Classification: 62F12; 62F40; 65M32; 74D05.

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“…While such approximations may be satisfactory for long time stress analyses, the neglect of loading phases produces significant errors in viscoelastic characterizations [95] [96]. In [53] it is stated that measurements of the loading times 1 t are subject to errors with larger errors corresponding to shorter 1 t times. The analysis is based on constant stress loadings without inclusion of loading cycles in the data analysis.…”

Section: ) Contributions Of the Loading Phase In Determining Materiamentioning

confidence: 99%

“…SV SV (53) With the mathematical model, one is again faced with a discontinuity due to the double valued Heaviside function at the temporal origin resulting in…”

Section: Svmentioning

confidence: 99%

Elastic and Viscoelastic Poisson’s Ratios: The Theoretical Mechanics Perspective

Hilton¹

2017

MSA

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A recent review publication presented an extensive and comprehensive assessment of the phenomenological relations of Poisson's ratios (PRs) to the behavior and responses of contemporary materials under specific loading conditions. The present review and analysis paper is intended as a theoretical mechanics complement covering mathematical and physical modeling of a single original elastic and of six time and process (i.e. path and stress) dependent viscoelastic PR definitions as well as a seventh special path independent one. The implications and consequences of such models on material characterization are analyzed and summarized. Indeed, PRs based on experimentally obtained 2-D strains under distinct creep and/or relaxation processes exhibit radically different time responses for identical material specimen. These results confirm the PR's implicit path dependence in addition to their separate intrinsic time reliance. Such non-uniqueness of viscoelastic PRs renders them unsuitable as universal material descriptors. Analytical formulations and experimental measurements also examine the physical impossibility of instantaneously achieving time independent loads or strains or their rates thus making certain PR definitions based on constant state variables, while mathematically valid, physically unrealistic and unachievable. A newly developed theoretical/experimental protocol for the determination of the time when loading patterns reach stead-state conditions based on strain accelerations demonstrates the capability to measure this time from experimental data. Due to the process dependent PRs, i.e. stress and stress history paths, the non-existence of a unique viscoelastic PR and of a universal elastic-viscoelastic correspondence principle or analogy (EVCP) in terms of PRs is demonstrated. Additionally and independently, the required double convolution integral construction of linear viscoelastic constitutive relations with the inclusion of PRs is cumbersome analytically and computationally needlessly highly CPU intensive. Furthermore, there is no theoretical fundamental hint as to what loading path is required to produce a unique universal viscoelastic PR definition necessary for formulating a PR based constitutive relation or an EVCP protocol. The analysis associated with an additional Class VII viscoelastic PR establishes it as a universal representation which is loading path and strain independent while still remaining time dependent. This Class PR can be the one used if it is desired to express constitutive relations in terms of PRs, subject to the caveat applying to all PR Classes regarding the CPU intensiveness in the time space due to triple product and double convolution integral constitutive relations. However, the use PRs is unnecessary since any set of material behavior can be uniquely and completely defined in terms of only moduli and/or compliances. The mathematical model of instantaneous initial loading paths, based on Heaviside functions, is examined in detail and shown to lead to infinite vel...

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Viscoelastic Materials

Cited by 760 publications

References 0 publications

Resistive Factors of the Blood Flow and Energy Distribution in the Body

Resistive Factors of the Blood Flow and Energy Distribution in the Body

Material parameter estimation and hypothesis testing on a 1D viscoelastic stenosis model: Methodology

Elastic and Viscoelastic Poisson’s Ratios: The Theoretical Mechanics Perspective

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